pointsByIntersection -- computes ideal of point set by intersecting maximal ideals

Synopsis

Usage:
pointsByIntersection(M,R)
Inputs:
- M, a matrix, in which each column consists of the coordinates of a point
- R, a polynomial ring, coordinate ring of the affine space containing the points
Outputs:
- a list, grobner basis for ideal of a finite set of points

Description

This function computes the ideal of a finite set of points by intersecting the ideals for each point. The coordinates of the points are the columns in the input matrix M.

i1 : M = random(ZZ^3, ZZ^5)

o1 = | 5 9 7 9 3 |
     | 9 4 4 0 5 |
     | 1 8 1 5 5 |

              3        5
o1 : Matrix ZZ  <--- ZZ

i2 : R = QQ[x,y,z]

o2 = R

o2 : PolynomialRing

i3 : pointsByIntersection(M,R)

                 2                                      2                    
o3 = {14y*z - 23z  + 70x + 14y + 131z - 710, 35x*z + 13z  - 245x - 84y - 372z
     ------------------------------------------------------------------------
                2      2                                         2        
     + 2165, 21y  + 76z  - 210x - 357y - 624z + 3110, 20x*y - 31z  - 10x -
     ------------------------------------------------------------------------
                         2     2                     3      2
     72y + 259z - 430, 7x  + 2z  - 84x - 26z + 269, z  - 14z  + 53z - 40}

o3 : List

Ways to use `pointsByIntersection` :

pointsByIntersection(Matrix,Ring)

pointsByIntersection -- computes ideal of point set by intersecting maximal ideals

Synopsis

Description

See also

Ways to use pointsByIntersection :

Ways to use `pointsByIntersection` :